This is a Phase II/III trial of two doses of dideoxyinosine (DDI) administered to children who have failed treatment with zidovudine. Treatment will continue until the last patient enrolled has received 52 weeks, and direct assessments will be made for tolerance and side effects of the two regimens, for the progression of HIV infection, and for the degree of change in neurodevelopmental disease. Comparisons will be made between groups for clinical, immunological, and virological parameters.